The light curves of variable DA white dwarf stars are usually
multi-periodic and non-sinusoidal. These light curve distortions provide
extra information about the pulsations, both physical and geometrical, that
is thrown away unless they are analyzed. The Fourier transforms of the
light curves show peaks both at eigenfrequencies of the pulsation modes and
at sums and differences of these frequencies. These combination
frequencies result from the distortions in the light curves. Several
theories provide a context for this analysis by predicting combination
frequency amplitudes. In these theories, the combination frequencies arise
from non-linear mixing in the outer layers of the white dwarf, so their
analysis cannot yield direct information on the global structure of the
star as eigenmodes provide. However, their sensitivity to mode geometry
does make them a useful tool for identifying the spherical degree of the
modes that mix to produce them.
In my thesis, I analyze data from eight hot, low-amplitude DAV
white dwarfs and measure the amplitudes of combination frequencies present.
By comparing these amplitudes to the predictions of the theory of Goldreich
and Wu, I have verified that the theory is crudely consistent with the
measurements. I have also investigated to what extent the combination
frequencies can be used to measure the spherical degree (ell) of the modes
that produce them. We find that modes with ell > 2 are identifiable as
high ell based on their combination frequencies alone. Distinguishing
between ell = 1 and 2 is also possible, using harmonics. These results
will be useful for conducting seismological analysis of large ensembles of
ZZ Cetis, such as those being discovered using the Sloan Digital Sky
Survey. Since this method relies only on photometry at optical
wavelengths, it can be applied to faint stars using modest sized
telescopes.
During the next phase of my thesis, I will observe ZZ Cetis with
the increased signal of the Southern Observatory for Astrophysical Research
(SOAR) 4.2-meter telescope for further verification of this photometric
mode identification method. The data I have analyzed thus far were
acquired with 1- to 2-meter telescopes at various locations. The SOAR
4.2-meter telescope will aid me in acquiring greater signal and the data
will reveal previously undetected combination frequencies.
The difficulty in classifying each pulsation mode has been holding
back theorists from analyzing white dwarf interiors. I will apply this new
photometric mode identification method to all of the SOAR data. The
improved asteroseismology of this database will provide a large sample of
stars. The data from these stars will help us better understand the
physics of white dwarf interiors.